Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices
Jean‐Charles Faugère, Chenqi Mou · 2011
Let I in K[x1,...,xn] be a 0-dimensional ideal of degree D where K is a field. It is well-known that obtaining efficient algorithms for change of ordering of Gröbner bases of I is crucial in polynomial system solving. Through the algorithm FGLM, this task is classically tackled by linear algebra operations in K[x1,...,n]/I. With recent progress on Gröbner bases computations, this step turns out to be the bottleneck of the whole solving process.